因数 64x^6-y^6

解

因数

64 x^{6} - y^{6}

(2 x + y) (4 x^{2} - 2 x y + y^{2}) (2 x - y) (4 x^{2} + 2 x y + y^{2})

解答ステップ

64 x^{6} - y^{6}

64 x^{6} = (8 x^{3})^{2}

y^{6} = (y^{3})^{2}

= (8 x^{3})^{2} - (y^{3})^{2}

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

(8 x^{3})^{2} - (y^{3})^{2} = (8 x^{3} + y^{3}) (8 x^{3} - y^{3})

= (8 x^{3} + y^{3}) (8 x^{3} - y^{3})

因数

8 x^{3} + y^{3} : (2 x + y) (4 x^{2} - 2 x y + y^{2})

= (2 x + y) (4 x^{2} - 2 x y + y^{2}) (8 x^{3} - y^{3})

因数

8 x^{3} - y^{3} : (2 x - y) (4 x^{2} + 2 x y + y^{2})

= (2 x + y) (4 x^{2} - 2 x y + y^{2}) (2 x - y) (4 x^{2} + 2 x y + y^{2})